How to make it so a part goes to where a player is looking?

You can move the piece to where the player's mouse is pointing, or where the player's head is pointing.

I will do it with the Mouse position, as it may be easier for your learning.

First, in LocalScript, when you activate RemoteEvent, remember to send LookVector Mouse, so that we can calculate the direction in which the projectile will be launched.

local Player = game.Players.LocalPlayer
local Mouse = Player:GetMouse()

local ReplicatedStorage = game:GetService("ReplicatedStorage")
local RemoteEvent = ReplicatedStorage:WaitForChild("RemoteEvent")

Mouse.Button1Down:Connect(function()
    local MouseLookVector = Mouse.Hit.LookVector

    RemoteEvent:FireServer(MouseLookVector )
end)

Now in ServerScriptService, to capture the Event

local ReplicatedStorage =  game:GetService("ReplicatedStorage")
local RemoteEvent = ReplicatedStorage:WaitForChild("RemoteEvent")
local Velocity = 100 -- you can change this whenever you want

local ServerStorage = game:GetService("ServerStorage")

RemoteEvent.OnServerEvent:Connect(function(Player, MouseLookVector)
    -- now i will use your code.
    local part = ServerStorage.Lazer:Clone()
    local BodyVelocity = Instance.new("BodyVelocity", part)

    part.Parent = workspace
    part.Position = Player.Character.Torso.Position
    part.CanCollide = false
    part.Anchored = true

    BodyVelocity.Velocity = MouseLookVector * Velocity
    -- To make the projectile go in the right direction

end)

I hope I helped, if you have any questions, you can ask me :)

Note: Your projectile cannot have Anchored = true, if Anchored is activated, BodyVelocity will have no effect on the body.